If f(x, y) = 4e*y cos (x- 1) , then the linear approximation at (1,0) is | (A) 4 + 16x (B) 4 + 4x (C) 4 + 16y (D) 8-4x + 16y (E) 4- 4y

Q: Estimate the area under the line y= 2x+1 using six rectangles and right endponits over the interval…

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Q: Show that the directiona f(x, y, z) = z²x + y ² at ( X (1/15" + ) ; 255. them

A: fx,y,z=z2x+y3 P1,1,2v→=15i+25j We know directional derivative Dv→fP=∇fP.v→v→

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Q: Find the directional derivatives of the convex function f(x) = max{−5x + 3, 2x + 1}.

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Q: A local target store bought 116 pizzas at Pizza Hut for its holiday party. Each guest ate 1/6 of a…

A: Let x be the number of pizzas bought by the store and y be the number of guests target have for the…

Q: 10. Find the derivative of y = V3x + 2. c) d) 3x a) 2V3x+2

A: Using derivatives

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A: Partial derivative of f w.r.t a variable is the indicator of the sensitivity of f towards that…

Q: The orthogonal trajectories of the family of curves y = cx² is (A) 2x +y2=k (B) x²+2y² = k © x=ky² D…

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Q: Determine when the following pairs of functions are linearly independent. (a) y1(t) = e"it; Y2(t) =…

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Q: ƒ(x, y) = x¹y — x²y³

A: Please see the below picture for detailed solution.

Q: Let h(æ, y) = f(x)g(y) + (9(y))² and suppose that f(1) = 5, f'(1) = 3, g(2) = 8, g'(2) = 10. Then…

A: Given function is - h(x,y) = f(x) g(y) + g(y)2             ............................(1)We have to…

Q: The gradient of f(x, y) = xy at (x, y) = ( – 3, – 2) is %3D

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Q: 12. Find the second derivative for the function f (x)=4x+12x²-20x-18 and solve the equation f"(x)=0.…

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Q: Find a linear approximation of the function f(x) = V1-x at a = 0. %3D

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Q: If f(x,y)=2y2ex+3ln(xy), find fxyy(1,1).

A: Given  fx,y = 2y2ex + 3lnxy                        fxx,y = ∂f∂x = 2y2 ∂∂xex + 3∂∂xlnxy…

Q: dz (е) dz

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Q: If f(x, y, z) = 2x5 + 3y5 - 8x3y²z², what is the partial derivative of f with respect to x? (A 10х4…

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Q: af , Given the function f (x,y) = 3x – x²y² + 2x°y, what is iTe ду А. 3 — 2ху? + бх?у В. - 2х3у +…

A: Given query is to find the partial derivative with respect to y.

Q: 3 f(x, y) = x° sin(xe")+ xe

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Q: Example If F[f(t)] =e/(1+f^2) find the F.T of F[f(2t)] 1+f2

A: Given:Fft=11+f2e11+f2To find:Ff2t

Q: 11) Find a function y-f (x) that satisfies both conditions: d - 6x -4x+5,f(-1) =3 dx %3D dy 2 3 ==+…

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